This talk explores various challenges associated with passive and port-Hamiltonian (pH) systems. The first part focuses on constructing pH systems from data, considering two principal strategies: preserving the pH structure throughout the construction process or enforcing this structure post hoc on an unstructured model. Building upon the Dynamic Mode Decomposition framework, we first adapt the underlying least-squares problem to incorporate the pH structure and propose a tailored optimization algorithm. Subsequently, we address the case where an unstructured (non-passive) model is given. To impose the pH structure — more generally, passivity — we develop a method that perturbs the system’s output matrix. This approach employs a novel parametrization of passive systems based on the KYP lemma and utilizes a gradient-based optimization technique to determine the perturbation. As the resulting optimization problem is non-convex, we propose strategies for avoiding or escaping local minima. In the second part, we present a new perspective on model order reduction (MOR) for pH systems by incorporating the approximation of the Hamiltonian. To this end, we extend the classical pH class by treating the Hamiltonian as an additional output, thereby falling within the broader class of linear systems with quadratic output. A two-stage MOR approach for the extended pH system is then proposed: first, conventional structure-preserving MOR is performed, followed by an optimization of the Hamiltonian formulated as a convex optimization problem. For each proposed method, numerical experiments are conducted to illustrate and validate the effectiveness and practical utility of the approaches.

tba

tba

An overall strategy for numerical simulations and optimization of fluid flows for industrial applications is introduced. The integrative approach takes advantage of numerical simulation strategies and newly developed mathematical optimization techniques, which a re all based on kinetic model descriptions and on Lattice Boltzmann Methods (LBM) as discretization strategies. Thereby, the resulting algorithms were implemented in a highly generic way in the open source framework OpenLB. In the talk, particular focus is placed on the design and application of the approach in order to face contemporary challenges in Computational Fluid Dynamics (CFD). Further, the consideration of LBM as a generic technique for the approximation of Partial Differential Equations (PDE) and its implementation for heterogeneous high performance computing (HPC) platforms are highlighted. The presented approaches and realizations are illustrated by means of various fluid flow simulation and optimization examples in many different engineering fields, where specific aspects are discussed for the simulation of particulate and turbulent flows as well as optimal control and optimization problems.